Two monochromatic sources of electomagnetic wave, `P` and `Q` emit waves of wavelength `lambda = 20 m` and separted by `5m` as shown. `A,B` and `C` are three points where interference of these waves is observed. If phase of a wave generated by `P` is ahead of wave generated by `Q` by `pi//2` then (given intensity of both waves is `l`) :

Options

A. phase difference of these waves at `B` is `180^(@)`
B. intensitiesat `A,B` and `C` are in the ratio `2 : 0 : 1` respectively
C. intensitiesat `A,B` and `C` are in the ratio `1 : 2 : 0` respectively
D. phase difference at `A` is `0^(0)`.

Answer

A, B, D

Explanation

Wave emitted from `Q , y = Asin (omegat - kx_(Q))`
Wave emitted from `P, y = Asin (omegat - kx_(P) + (pi)/(2))`
`Deltaphi = phi_(P) - phi_(Q) = omegat - kx_(P) + (pi)/(2) - (omegat - kx_(Q)) , .C`
`= k (x_(Q) - x_(P)) + (pi)/(2)`
`= (2pi)/(lambda)(x_(Q) - x_(P)) + (pi)/(2)`
`= (pi)/(10)(x_(Q) - x_(P)) + (pi)/(2))`

For `A x_(Q) - x_(P) = -5 rArr Deltaphi = (pi)/(10)(-5) + (pi)/(2) = 0`
For `B x_(Q) - x_(P) = 5`
`rArr Deltaphi = pi`
For `C x_(Q) - x_(P) = 0`
`rArr Deltaphi = (pi)/(2)`
`I_(A) : I_(B) : I_(C) = (I + I + 2cos0) : (I + I + 2Icospi) : (I + I + 2Icos"(pi)/(2))`